The original circle x2+y2−6x−10y+30=0 has centre C=(3,5),‌‌‌ radius ‌r=√32+52−30=√4=2. We reflect the centre across the line 2x+y−2=0 Reflection formula gives the image point C′(x′,y′) : d=‌
2(3)+1(5)−2
22+12
=‌
9
5
. Thus, x′=3−2(2)(‌
9
5
)=3−‌
36
5
=−‌
21
5
y′=5−2(1)(‌
9
5
)=5−‌
18
5
=‌
7
5
So the image centre is C′=(−‌
21
5
,‌
7
5
). Radius remains 2 . Its equation is: (x−x′)2+(y−y′)2=4.